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Schrödinger Equations in Nonlinear Systems

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Schrödinger Equations in Nonlinear Systems/ by Wu-Ming Liu, Emmanuel Kengne.
作者:	Liu, Wu-Ming.
其他作者:	Kengne, Emmanuel.
面頁冊數:	XVI, 569 p. 251 illus., 201 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Physics. -
電子資源:	https://doi.org/10.1007/978-981-13-6581-2
ISBN:	9789811365812

Schrödinger Equations in Nonlinear Systems
Liu, Wu-Ming.

Schrödinger Equations in Nonlinear Systems[electronic resource] /by Wu-Ming Liu, Emmanuel Kengne. - 1st ed. 2019. - XVI, 569 p. 251 illus., 201 illus. in color.online resource.

Overview of nonlinear Schrödinger equations -- Well-posedness of nonlocal boundary value problems and Schrödinger equations -- Nonlinear Schrödinger equations of single transmission lines -- Derivative nonlinear Schrödinger equations for single transmission lines -- NLS equations for the system of the nonlinear transmission line coupled by capacitor C₂ -- Inhomogeneous nonlinear Schrödinger equations of Bose-Einstein condensates with two-body interactions.

This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.

ISBN: 9789811365812

Standard No.: 10.1007/978-981-13-6581-2doiSubjects--Topical Terms:

564049
Physics.

LC Class. No.: QC5.53

Dewey Class. No.: 530.15

Schrödinger Equations in Nonlinear Systems
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520 $a This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.
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